The importance of a beautiful tone,
the fine tonal balance, can never be overlooked.

What is tone? Tone is the
natural sound of the instrument - the primary pitch plus the overtones (harmonic
series), combined with the performer's particular technique of playing.

The tone of a piano is affected by a number of
different factors. Firstly, there is the piano itself - different makes,
different model or sizes of piano have different tones. Secondly, a piano, like
any instrument, can sound like a different instrument in the hands of different
players. The better the pianist the better the tone. This is because tone
is more than something determined by fixed acoustical properties of the
instrument itself, it is also determined by the touch habits of the piano
player.

Why the tone is determined by the touch habits of the
player? As we have discussed in The Piano, the overtones
that a metal string generates depending on the speed of the activated hammer.
The kinetic energy of the hammer is transmitted from the energy that the piano
player delivered to the key. Depressing the same key from different height, with
different speed or weight produces the same primary pitch but also produces
different overtones resulting in different tonality.

To present a theoretical analysis of the
tone, we
start with the energies that produce the tone. For those who don't understand the formula,
skip it and just grasp the results and apply them to
your piano playing.

The Energies Generated by the Key Descent:

There are two kinds of energies: Potential Energy and
Kinetic Energy, the first is the energy due to the position of the
object; the latter due to the movement of the object. Their familiar physics
formulas are the following:

h high (in this case: the distance between the hand and the key surface)

Kinetic Energy: KE =
2 mv*v

where: m mass (in our case: the upper arm, forearm, hand or finger)

v velocity or speed ( in our case: the speed of key descend)

As we know,
g is the
gravitational acceleration. since it is a constant, we are not interest in it.
We are only interested in the variables : m, v and h. By changing
them , we can produce a wide arrange of sound and tones out of the piano, raging
from pianissimo to fortissimo; from the softest, warmest to the loudest,
hardest.

The h, m and v are briefly mentioned
in the "Art of piano playing"by the famous Russian piano pedagogue Heinrich Neuhaus, but it is not clearly
defined there. With my physics background, I try to define and discuss them
here:

Thevand h are somehow related.

In Slow to Moderate Tempo:

We can utilize the
potential energy, let
the weight of different parts of our arm freely fall from a certain
h (not too high!) only by the force of gravity alone without any
muscular effort. The potential energy is the main source of
energy in this case. The higher the h, the greater the v,
thus the greater the sound. Because the energy generated by this v is transferred to the hammer's kinetic energy resulting in the greater speed of the hammer
hitting the string. However, this higher h only applied to a
slow to moderate tempo.

In Fast Tempo:

"In
rapid playing there is no time to lift high and strike. The fingers must
remain near to the keys. The tone made by striking is not agreeable to me."

-- Vladimir Horowitz:
"Technic the Outgrowth of Musical Thought"

The v
not only can be generated by the
h but also can be generated by the muscular effort which is the
main source of energy in a fast tempo.
When we play fast and loud , there is no time to
waste on the higher h. We need to play close to the key. In
order to generate the v, we throw our hand into play position
with the help of our upper arm, forearm and the wrist, just like a
whip (see The Pianist and
The Technique). The shoulder joint is
the handle of the whip, the fingers - the tip of the whip. The
kinetic energy of this v is generated by the contraction
of the strong shoulder and chest muscles and is transferred to the
hammer's kinetic energy.

Sometimes the h would become zero.
Especially in playing big chords, we place our hand on the surface
of the key and suddenly contract some of the strongest body and arm
muscles- A press (push) against the key bed (just for a split
second, please!) This can cause the great speed in key descent thus
the great speed of the hamper hitting the string.

Extreme h and v will cause the string to
generate unpleasant overtones, thus resulting in a harsh sound and poor tone
quality. Some piano players habitually strike the key. The sound produced by
this habit is harsh and not agreeable. We should always avoid.

"There is a
pianist who is an excellent musician and a master of his art, but I
have one objection to make to his playing: h and v are exaggerated"

-- Heinrich
Neuhaus: "The Art of Piano Playing"

The m:

The m could be the weight of our upper arm, forearm,
hand, fingers or any combined, blended muscular activities. Smaller m generates softer sound, bigger
m generates louder sound. There could be
different combination of our four components (see
The Pianist ).
Sometimes we feel that our arm is heavy and the fingers are firm and passive;
Sometimes we feel our arm is light and passive, like floating in the air and the
fingers are active. etc.

CONCLUSIONS:

Based on the above theoretical analysis of
tone, we come to the following conclusions:

1) When the m is big and the v and h
is small, you produce a rich, deep, sonorous sound like the sound
from the big church bell; When the m is small and the v and
h are moderate, you produce a vivid, pearly sound like the
sound of the little bell; when the m is big and the v and
the h are high, you produce a loud, harsh sound like a bang.

2) By varying the m, v and h, We can
literally produce a wide range of volumes and sonorities, create nuances
and dynamics in music. Of course, we need to practice, experiment it on
the piano consciously and distinctly.

"In searching for tone
quality - the second of the most difficult factor in playing -- It is
helpful to think of the instruments of the orchestra.... if one thinks
of the quality or the sonority of the various instruments, one is helped
to play more beautifully."